+14 An equilateral triangle is constructed on each side of a square with side length 2. The four outer vertices are then joined to form a large square. Find the side length of the large square.
The height of an equilateral triangle with side length 2 is √3. This can be found using the Pythagorean Theorem, or by realizing that the height of the equilateral triangle is the altitude of the square, which is also the side length of the square divided by √2.
The side length of the large square is equal to the sum of the side length of the small square, the height of the equilateral triangle, and the side length of the equilateral triangle. This is equal to 2 + √3 + 2 = 2 + √3 + 2 = 4 + √3.
Therefore, the side length of the large square is 4 + √3.
+170 We can calculate the diagonal of the square, which is \(2+2\sqrt3\). Square and divide by two to get your answer of \(\boxed{8+4\sqrt3}\)
